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I have a question that I don't know what to tag with, because I want to know what it is. It sounds a bit vague; I will just post my question to make it clearer:

Title: What is name of equations that accept division by zero?

Body:

They might not have a name; they just popped in my head, and I found out that they are useful in a way; I am interested in more information about them by knowing their name.

An equation for example:

$f(x) = nx$

$f'(x) = (f(x+0)-f(x))/0 = (nx+0n-nx)/0 = (0n)/0 = n$

More hardcore one:

$f(x) = a^x$

$f'(x) = (f(x+0)-f(x))/0 = (a^{x+0}-a^x)/0 = (a^x(a^0-1))/0 = (a^x(e^{\ln(a^0)}-1))/0 = (a^x(e^{0\ln(a)}-1))/0$

Place $e^x = 1 + x + x^2/2 + ... + x^k/!k$ in $f'(x)$.

$f'(x) = (a^x(1 + 0\ln(a) + ... - 1))/0 = (a^x(0\ln(a) + ...))/0 = a^x(\ln(a) + (...)/0)$

Discard values that are $0$ that we can't rescue them with that $/0$.

$f'(x) = a^x(\ln(a)) = a^x\ln(a) $

This is not limit, but normal mathematics that don't panic in front of a $/0$.

Tags: [nonstandard-analysis] [limits] [infinitesimals] Those are the tags that gave me the impression from the comments that I need to use.

Is it acceptable in the main site? Do I need to choose different SE site? If it's acceptable, then what are the tags that is required to submit such question?

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    $\begingroup$ The reason we have formalized limits is for that exact purpose (derivatives). Also, there are no non-negative numbers that are less than zero. The problem with what you've suggested is that it does not lead to well-defined results. I would vote to close the proposed question as "unclear as to what you are asking." $\endgroup$ – apnorton Nov 23 '14 at 3:25
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    $\begingroup$ I would suggest reading about non-standard analysis and then asking a focused question. That said, +1 to this question, for asking on meta first. $\endgroup$ – user147263 Nov 23 '14 at 3:26
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    $\begingroup$ I'd upvote this were it on main, since I think it could be begetting of a good answer and I think it's a really really common train of thought that plenty of people would benefit from an answer of (and an answer better than "no, you can't divide by zero"). That said, I think a stronger question would be to ask about how such things are formalized - since that gives answers a pretty clear purpose. (In any case, whatever it is that you're really trying to ask with this question is on-topic if you ask it well) $\endgroup$ – Milo Brandt Nov 23 '14 at 4:43
  • $\begingroup$ @anorton Thanks for your feedback; I improved that part, is it any better now? I don't understand the well-define result part. If I will add that those equations made to work around the division by zero, then will it work? $\endgroup$ – KugBuBu Nov 23 '14 at 12:11
  • $\begingroup$ @Rafflesiaarnoldii Thanks; it helped me find some tags. $\endgroup$ – KugBuBu Nov 23 '14 at 12:23
  • $\begingroup$ @Meelo Looks like it will be more interesting like that while getting the name too; thanks I will edit later. $\endgroup$ – KugBuBu Nov 23 '14 at 12:46
  • $\begingroup$ math.stackexchange.com/questions/1035282/… posted the question, thanks everyone. By the way I posted in this account by accident, this is not mine. (The other one in the question is mine) $\endgroup$ – KugBuBu Nov 23 '14 at 17:04
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Aside from the suitability of the question proposed above:

In general it is okay to ask about names of things and identifying objects. Please tag them with and/or as appropriate.

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